Current-potential curves determination

The potential dependence of the velocity of an electrochemical phase boundary reaction is represented by a current-potential curve I(U). It is convenient to relate such curves to the geometric electrode surface area S, i.e., to present them as current-density-potential curves J(U). The determination of such curves is represented schematically in Fig. 2-3. A current is conducted to the counterelectrode Ej in the electrolyte by means of an external circuit (voltage source Uq, ammeter, resistances R and R") and via the electrode E, to be measured, back to the external circuit. In the diagram, the current indicated (0) is positive. The potential of E, is measured with a high-resistance voltmeter as the voltage difference of electrodes El and E2. To accomplish this, the reference electrode, E2, must be equipped with a Haber-Luggin capillary whose probe end must be brought as close as possible to... 

In general, according to Eq. (2-10), two electrochemical reactions take place in electrolytic corrosion. In the experimental arrangement in Fig. 2-3, it is therefore not the I(U) curve for one reaction that is being determined, but the total current-potential curve of the mixed electrode, E,. Thus, according to Eq. (2-10), the total potential curve involves the superposition of both partial current-potential curves ... 

It must be emphasised that in evaluating the limiting cathode potential to be applied in the separation of two given metals, simple calculation of the equilbrium potentials from the Nernst Equation is insufficient due account must be taken of any overpotential effects. If we carry out, for each metal, the procedure described in Section 12.2 for determination of decomposition potentials, but include a reference electrode (calomel electrode) in the circuit, then we can ascertain the value of the cathode potential for each current setting and plot the current-potential curves. Schematic current-cathode potential... 

The current-potential curve of a mixture of couples can be obtained by adding algebraically, at any potential, the currents given by each of the couples present, provided these have been determined in circumstances that correspond to those in the mixture. 

In voltammetry (abbreviation of voltamperometry), a current-potential curve of a suitably chosen electrochemical cell is determined, from which qualitative and/or quantitative analytical data can be obtained. 

The basic theory of mass transfer to a RHSE is similar to that of a RDE. In laminar flow, the limiting current densities on both electrodes are proportional to the square-root of rotational speed they differ only in the numerical values of a proportional constant in the mass transfer equations. Thus, the methods of application of a RHSE for electrochemical studies are identical to those of the RDE. The basic procedure involves a potential sweep measurement to determine a series of current density vs. electrode potential curves at various rotational speeds. The portion of the curves in the limiting current regime where the current is independent of the potential, may be used to determine the diffusivity or concentration of a diffusing ion in the electrolyte. The current-potential curves below the limiting current potentials are used for evaluating kinetic information of the electrode reaction. 

The film electrodeposition process was studied by means of linear sweep voltammetry. The rate of electrochemical reaction was determined from current density (current-potential curves). The film deposits were characterized by chemical analysis, IR - spectroscopy, XRD, TG, TGA and SEM methods. 

The transfer coefficient a has a dual role (1) It determines the dependence of the current on the electrode potential. (2) It gives the variation of the Gibbs energy of activation with potential, and hence affects the temperature dependence of the current. If an experimental value for a is obtained from current-potential curves, its value should be independent of temperature. A small temperature dependence may arise from quantum effects (not treated here), but a strong dependence is not compatible with an outer-sphere mechanism. 

The transfer coefficient determines the symmetry - or lack thereof - of the current-potential curves they are symmetric for a = 1/2. For this reason the transfer coefficient is also known as the symmetry factor. 

There are two mains aspects of the role of dimerization of intermediates on the electrochemical responses that are worth investigating in some detail. One concerns the effect of dimerization on the primary intermediate on the current-potential curves that corresponds to the first electron transfer step, the one along which the first intermediate is generated. Analysis of this effect allows the determination of the dimerization mechanism (radical-radical vs. radical-substrate). It is the object of the remainder of this section. 

In cyclic voltammetry, the current-potential curves are completely irreversible whatever the scan rate, since the electron transfer/bond-breaking reaction is itself totally irreversible. In most cases, dissociative electron transfers are followed by immediate reduction of R, as discussed in Section 2.6, giving rise to a two-electron stoichiometry. The rate-determining step remains the first dissociative electron transfer, which allows one to derive its kinetic characteristics from the cyclic voltammetric response, ignoring the second transfer step aside from the doubling of the current. 

Figure 4.14b and c illustrate the possibility of using convolution (Section 1.3.2) to transform all the voltammograms, whether they are plateau- or peakshaped, into a plateau-shaped wave. Measuring the height of this plateau allows determination of the kinetic constant, showing that this does not necessarily require that the raw current-potential curve be plateau-shaped. The standard potential, FpQ, may also be determined this way. 

In the case of cyclic voltammetry, too, amplification of the current upon addition of the substrate may be exploited to determine the kinetic characteristics of the electrode electron transfer. Replacing Nemst s law by a kinetic law and assuming, as already discussed, that dr /dt is negligible, the dimensionless current-potential curves are given by... 

A preliminary electrochemical overview of the redox aptitude of a species can easily be obtained by varying with time the potential applied to an electrode immersed in a solution of the species under study and recording the relevant current-potential curves. These curves first reveal the potential at which redox processes occur. In addition, the size of the currents generated by the relative faradaic processes is normally proportional to the concentration of the active species. Finally, the shape of the response as a function of the potential scan rate allows one to determine whether there are chemical complications (adsorption or homogeneous reactions) which accompany the electron transfer processes. 

SWV experiments are usually performed on stationary solid electrodes or static merciuy drop electrodes. The response consists of discrete current-potential points separated by the potential increment AE [1,20-23]. Hence, AE determines the apparent scan rate, which is defined as AE/t, and the density of information in the response, which is a number of current-potential points within a certain potential range. The currents increase proportionally to the apparent scan rate. For better graphical presentation, the points can be interconnected, but the fine between two points has no physical significance, as there is no theoretical reason to interpolate any mathematical function between two experimentally determined current-potential points. The currents measured with smaller A are smaller than the values predicted by the interpolation between two points measured with bigger AE [3]. Frequently, the response is distorted by electronic noise and a smoothing procedure is necessary for its correct interpretation. In this case, it is better if AE is as small as possible. By smoothing, the set of discrete points is transformed into a continuous current-potential curve. Care should be taken that the smoothing procedttre does not distort the square-wave response. 

Steady-State Kinetics, There are two electrochemical methods for determination of the steady-state rate of an electrochemical reaction at the mixed potential. In the first method (the intercept method) the rate is determined as the current coordinate of the intersection of the high overpotential polarization curves for the partial cathodic and anodic processes, measured from the rest potential. In the second method (the low-overpotential method) the rate is determined from the low-overpotential polarization data for partial cathodic and anodic processes, measured from the mixed potential. The first method was illustrated in Figures 8.3 and 8.4. The second method is discussed briefly here. Typical current—potential curves in the vicinity of the mixed potential for the electroless copper deposition (average of six trials) are shown in Figure 8.13. The rate of deposition may be calculated from these curves using the Le Roy equation (29,30) ... 

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

If we measure a residual current-potential curve by adding an appropriate supporting electrolyte to the purified solvent, we can detect and determine the electroactive impurities contained in the solution. In Fig. 10.2, the peroxide fonned after the purification of HMPA was detected by polarography. Polarography and voltammetry are also used to determine the applicable potential ranges and how they are influenced by impurities (see Fig. 10.1). These methods are the most straightforward for testing solvents to be used in electrochemical measurements. 

The rate of deposition and the mixed potential are determined on the basis of the mixed-potential theory using the Evans diagram. First, the current-potential curve... 

In this section, the subtractive multipulse techniques DMPV and SWV are applied to reversible ion transfer across different liquid-liquid systems with one or two polarizable interfaces. These electrochemical techniques allow the accurate and easy determination of standard potentials directly from the peak potentials of the current-potential curves since non-faradaic and background currents are minimized [12, 35-40]. 

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